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Concepts and VocabularyChapter 2 Review Concepts and Vocabulary
Q1. If a function is defined by the equation y = f(x), then x is called the _?_ variable and y is the _?_ variable.
A1. independent dependent
Q2. A set of points in the xy-plane is the graph of a function if and only if every _?_ line intersects the graph in at most one point.
Q3. The set of all images of the elements in the domain of a function is called the _?_.
Q4. True or False: Every relation is a function.
Q5. True or False: The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0).
Q6. True or False: The independent variable is sometimes referred to as the argument of the function.
Q7. For the graph of the linear function f(x) = mx + b, m is the _?_ and b is the _?_.
A7. slope y-intercept
Q8. True or False: The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1, inclusive.
Q9. The average rate of change of a function equals the _?_ of the secant line.
Q10. A function f is _?_ on an open interval if for any choice of x1 and x2 in the interval, with x1<x2, we have f(x1) < f(x2).
Q11. An _?_ function f is one for which f(-x) = f(x) for every x in the domain of f.
Q12. An _?_ function f is one for which f(-x) = -f(x) for every x in the domain of f.
Q13. True or False: Even functions have graphs that are symmetric with respect to the origin.
Q14. The graph of f(x) = mx + b is decreasing if m is _?_ than zero.
Q15. When functions are defined by more than one equation, they are called _?_ functions.
The cube function is odd and is increasing on the interval (- ∞, ∞).Q16. True or False: The cube function is odd and is increasing on the interval (- ∞, ∞).
Q17. True or False: The domain and range of the reciprocal function are the set of all real numbers.
Q18. Given f(x), then the graph of y = f(x – 2) may be obtained by a(n) _?_ shift of the graph of f a distance of 2 units to the _?_.
A18. horizontal right
Q19. Given f(x), then the graph of y = f(-x) may be obtained by a reflection about the _?_-axis of the graph of the function y = f(x).
Q20. Given f(x), then the graph of y = 3f(x) may be obtained by a vertical _?_ of the graph of f by a factor of _?_.
A20. stretch 3
Q21. True or False: The graph of y = - f(x) is the reflection about the x-axis of the graph of y = f(x).
Q22. True or False: To obtain the graph of y = f(x+2) – 3, shift the graph of y = f(x) horizontally to the right 2 units and vertically down 3 units.
Q23. True or False: To obtain the graph of y = f(4x), horizontally compress the graph of y = f(x) by a factor of 4 . That is, divide each x-coordinate on the graph of y = f(x) by 4.
Q24. If the domain of f is all real numbers in the interval [0,7], and the domain of g is all real numbers in the interval [-2,5], then the domain of f + g is all real numbers in the interval _?_.
Q25. The domain of f/g consists of all real numbers x for which g(x) _?_ 0 that are in the domains of both _?_ and _?_.
A25. ≠ f g
If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³ .Q26. If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³ .
Q27. True or False: f(g(x)) = f(x)· g(x)
Q28. True or False: The domain of (f· g)(x) consists of the numbers x that are in the domains of both f and g.
Q29. True or False: The domain of the composite function (f ◦ g)(x) is the same as the domain of g(x).
What is the best way to study for a Math test?Q30. What is the best way to study for a Math test?
A30. Work problems!
Objective - To graph linear equations using the slope and y-intercept.
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